Seesaw balance problem

In summary, in order to balance a 10m board with a 70kg adult and a 30kg child sitting on each end, the pivot point should be placed at a distance of 5m from the child. This can be determined using the equation Etorqueccw=Etorquecw, where x is the distance from the pivot point to the child and L is the length of the board.
  • #1
answerseeker
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A 70kg adult sits at one end of a 10m board, on other end sits a 30kg child. where should pivot point be placed so board is balanced? board's mass is 15kg.

so far, i have pivot point is 15kg(9.8)=147N (5) <-- half the board length.. for adult i have 686N and kid is 294N. i know that Etorqueccw=Etorquecw ... but I am not sure how to use that for the lengths of both humans, since there are 2 variables. need two eqns then rite? but what's the other eqn?..:confused:
 
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  • #2
You (should) have one equation and one unknown. Basically, suppose x is the distance from the pivot point the child. Then the distance to the adult from the pivot point is L - x where L is the length of the board. Put it into your torque equation and solve for x.
 
  • #3


Thank you for sharing this problem. I would approach this problem by first understanding the concept of torque. Torque is the measure of the force that causes an object to rotate around an axis or point. In this case, the seesaw board is the object and the pivot point is the axis. The torque exerted by the adult and the child must be equal for the board to be balanced.

To solve this problem, we need to set up two equations using the concept of torque. The first equation is the sum of the torques on the board, which should be equal to zero for the board to be balanced. The second equation is the torque exerted by the adult and the child, which should be equal to each other.

Let's start with the first equation. The torque exerted by the adult can be calculated by multiplying their weight (686N) by their distance from the pivot point. Since the pivot point is placed at 5m from the adult, the torque exerted by the adult is 686N x 5m = 3430Nm. Similarly, the torque exerted by the child can be calculated by multiplying their weight (294N) by their distance from the pivot point. Since the pivot point is placed at 5m from the child, the torque exerted by the child is 294N x 5m = 1470Nm.

Now, let's set up the second equation. As you mentioned, the torque exerted by the adult (3430Nm) must be equal to the torque exerted by the child (1470Nm). This can be represented as:

3430Nm = 1470Nm

Since both torques are equal, we can set them equal to each other and solve for the pivot point distance (r):

686N x r = 294N x (10m-r)

By solving for r, we get r = 1.96m. This means that the pivot point should be placed at 1.96m from the side where the adult is sitting and at 8.04m from the side where the child is sitting.

I hope this explanation helps. As scientists, it is important for us to use mathematical equations and principles to solve problems and understand the world around us. Keep up the good work!
 

1. How does a seesaw balance problem occur?

Seesaw balance problems occur when the weight on one side of the seesaw is greater than the weight on the other side, causing one side to be lower and the other side to be higher.

2. What factors affect the balance of a seesaw?

The balance of a seesaw is affected by the weight and distance from the fulcrum on each side. The heavier the weight and the further the distance from the fulcrum, the greater the force and the lower that side of the seesaw will be.

3. How can the seesaw balance problem be solved?

The seesaw balance problem can be solved by adjusting the weight or distance from the fulcrum on each side. If one side is lower, adding weight or moving the weight closer to the fulcrum will balance it out.

4. Can the seesaw balance problem be solved using math?

Yes, the seesaw balance problem can be solved using the principles of physics and mathematics. By calculating the weight and distance on each side, the seesaw can be balanced by adjusting these factors accordingly.

5. Are there any safety concerns related to the seesaw balance problem?

Yes, there can be safety concerns with seesaw balance problems, especially if the weight difference is significant. It is important to ensure that the seesaw is properly balanced before use to prevent accidents or injuries.

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